Dealing with children who have developed tinnitus is a challenge. There's just not that much data out there in the scientific literature about how to help them. An eleven year old boy in the UK had particularly difficulty with insomnia:
An 11-year-old with severe tinnitus is finally able to get a good night’s sleep after discovering listening to birds relieves his symptoms. Leo Bamford has suffered from the condition - which leaves him with a constant high-pitched ringing in his ears - since he was a toddler.  Every night the noise kept him awake for hours and left him tired and groggy in the morning.
Interestingly, a unique tinnitus masker was eventually able to help him deal with his sleep issues:
At the hospital he met hearing specialist Dr David Baguley who prescribed the sound box. The device is a small box with a digital recording of common garden birds singing which Leo can play and control as he wants. He has also been taught techniques to help manage the condition, like focusing on a particular sound so that his brain learns to ignore the tinnitus. Leo said: ‘It’s very high pitched and it’s always the same noise. It’s very annoying but most of the time I ignore it. ‘But there’s no other sounds at night, so I used to just lie there listening to it. ‘Now I turn on my bird box and I can get to sleep. I don’t have to listen to the noise at night anymore - it really helps. I’m so happy it’s working.’